Work and Energy Legacy Problem #14 Guided Solution
Problem*
Chloe leads South’s varsity softball team in hitting. In a game against New Greer Academy this past weekend, Chloe slugged the 181-gram softball so hard that it cleared the outfield fence and landed on Lake Avenue. At one point in its trajectory, the ball was 28.8 m above the ground and moving with a speed of 19.7 m/s. Determine the total mechanical energy of the softball.
Audio Guided Solution
A good problem solver is always reliant upon their understanding of physics concepts and math relationships in order to plot strategies for getting from known quantities to the unknown quantity. Here, the unknown quantity is the total mechanical energy, and the known quantities are the mass of a softball, m equal 181 grams, the speed of a softball, v equal 19.7 meters per second, and the height of the softball, h equal 28.8 meters. We wish to find, from this information, the total mechanical energy. We understand total mechanical energy to simply be the sum of the two forms of mechanical energy, the sum of the kinetic energy plus the potential energy. To so define the total mechanical energy, we'll need to first calculate the k e and the p e. So for the k e, I'm going to go one half m v squared, but the m here is given in grams, so I'll need to convert that to kilograms, 0.181 kilograms, and then I'll go one half times 0.181 kilograms times 19.7 squared, and when I do, I get 35.1221 joules as my kinetic energy. I'm going to write that down. The p e can be found with the equation p e equal g h, where once more, the m is 0.181 kilograms, the g is 9.8 newtons per kilogram, and the h is 28.8 meters. Multiplying, I get 51.0854 joules. Now what I need to do is add the k e to the p e. That will give me 86.2075 joules, and then I'll round to the three significant digits, such that the answer is 86.2 joules.
Solution
86.2 J
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{v}{v,velocity}_\descriptive{o}{o,original} = 0 \unit{\meter\per\second}\); \(\descriptive{a}{a,acceleration} = 4.2\unit{\meter\per\square\second}\); \(\descriptive{v}{v,velocity}_\descriptive{f}{f,final} = 22.9 \unit{\meter\per\second}\); \(\descriptive{d}{d,distance} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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